Okay... let's try this again with pictures for illustration.
The instructions outside of the room in the open book (double-click it) tell you what you need to know, but I'll reiterate it here... once your gem is activated, and you enter the first room, it will begin to shift colors. Your goal is to neutralize the gem, bringing it back to gray.
White (Cold) and Pink (Warm) are opposites.
Blue (Freezing) and Red (Blazing) are opposites.
Orange (Cure) and Green [noted in room 3 as light green] (Poison) are opposites.
Dark Orange (Greater Cure) and Dark Green (Lethal) are opposites.
The first room, you will only have to neutralize the gem a few times (randomly seems to be about 5 to 7 times). The second room, the speed seems to increase slightly, and you'll have to neutralize the gem randomly about 8 to 14 times. The third room will probably seem to go on forever, and the pace is yet a little faster (or maybe it just seems that way... I can't both do the puzzle and time it... hehe).
Once you finish the third room, you cross into the final room and either drop your gem onto the gold chest or just double-click the gold chest... either way, you get yourself a nifty prize!
Now how to do it.
First, make sure you are mounted... this is a fast pace puzzle that gets quicker as it goes.
Second, make sure you place your gem in a bag by itself, and out of the way (so you don't accidentally close it), with nothing around it so that you're not distracted as it changes color.
Also, I would suggest setting an OPEN DOOR macro for running quickly between rooms.
ROOM 1
In each of the pictures (above and those that follow), I position myself in the square marked center position. In the first and third rooms, they are marked with glowing runes on the ground.
When the gem turns white, I run diagonally to the pink (cold gem to warm square).
When the gem turns pink, I run diagonally to the white (warm gem to cold square).
When the gem turns blue, I run due west to the red (freezing gem to blazing square).
Note, that in none of my encounters has the gem ever turned red.
After you get into the appropriate space, WAIT UNTIL THE GEM TURNS GRAY AGAIN!!! This is important because if you mistime it and run back out of the space before the gem neutralizes, it'll probably kick you. Use this run out to color, back to "center position" strategy for each room.
ROOM 2
To me, this is the easiest of the rooms because unlike the other two, you really never have to break out into a full run.
Gem turns green, take a couple of steps diagonally to orange (poison gem to cure).
Gem turns white, take a couple of steps diagonally to pink (cold gem to warm).
Gem turns blue, take a couple of steps diagonally to red (freezing gem to blazing).
Gem turns pink, take a couple of steps diagonally to white (warm gem to cold).
Gem turns orange, take a couple of steps due east to green (cure gem to poison).
Again, I've never had the gem turn red.
ROOM 3
This is, by far, the hardest of the rooms, but taking up the tactic of the first room will work best (and yeah, it may take some time to get used to movement, and if you miss by a couple of tiles on a run back, don't worry so much about it, simply focus on direction... this stage is frantically paced). The center position (where all your moves should be based from) is again marked by a glowing rune.
If the gem turns dark green or orange, you can run along the same diagonal...
Gem turns dark green, few steps to dark orange (lethal gem to greater cure).
Gem turns orange, run to light green (cure gem to poison).
If the gem turns blue or pink, you can run along the same diagonal...
Gem turns pink, few steps to white (warm gem to cold).
Gem turns blue, run to red (freezing gem to blazing).
If the gem turns dark orange or light green, you can run along the same path west...
Gem turns light green, few steps due west to orange (poison gem to cure).
Gem turns dark orange, run due west to dark green (greater cure gem to lethal).
And if the gem turns white, simply run due east to pink (cold gem to warm).
Once again, I've never had the gem turn red.
The rooms get progressively difficult, but I've found that this strategy works the best for me... hope it's helpful for others!!!